However, I do a lot of editing of large digital photos, and I'm converting a second computer, with the exact same specifications as this one, to Xubuntu 13.10, AND I'm replacing the 128 MB memory module with a 1 GB module, giving me a total of 2 GB. I have read a lot of posts here that say with 2 GB it is best to go with the 32 bit download of 13.10. But I have also read a lot of posts here that say it's best to go with the 64-bit. That 2 GB is plenty to run 64-bit software, and that 32 bit software is rapidly becoming obsolete.

5 Answers
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Anything in the x86 Family is a 32-bit processor. You need to install the 32bit version.

If you had a AMD64 or x86_64 Family it would be a 64bit processor and capable of running a 64bit version.

As for the memory issue. The main difference between 32bit and 64bit is the ability to address more memory. A 32-bit processor can only handle up to 4GB or 2^32 = 4GB. A 64-bit can handle much more than that 2^64 = 16EB = 17,179,869,184. The implementation details are much more complex than this description.

Therefore the 64bit version of Xubuntu may be an option for you. With 2gb of ram you absolutely can happily run a 64bit operating system though you may find it consumes a little more of your ram than a 32bit install.

No, some models of Pentium 4 since Prescott have x86_64 instruction set
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Lưu Vĩnh PhúcMar 1 '14 at 2:05

I stand corrected. Some Pentium 4 cpus from around 2006 such as some of the ones in the HT line were X86-64. HT=Hyper Threading. Basically the last ones before the Intel Core2 series was pushed out in time for Vista's unveiling.
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mangoMar 1 '14 at 2:36

If your processor really is 64-bit capable (try booting from 64-bit LiveCD), I still think 64-bit system will give you no benefits.

64-bit systems may use more than 64GB, 32-bit with PAE (http://en.m.wikipedia.org/wiki/Physical_Address_Extension) may use up to 64 GB, without PAE -- up to 4GB. Those amounts of memory include not just physical memory, but virtual memory as well, so you cannot enlarge swap file or swap partition to overcome the limits.

Even a PAE 32-bit system can NOT allocate more than 4GB (memory and address space) to a single app, so apps that deal with huge amounts of data sometimes require 64-bit.

Generally if you compare the 32- and 64- bit versions of the same OS or of the same app, 64-bit one will use more memory due to larger size of primitive datatypes (mostly pointers). Which one will be faster, depends on application.

So, if you do not have much memory, and do not have apps that need more than 4GB of memory or of address space, 32-bit system is quite ok. 64-bit one is usually needed for systems with a lot of memory. However, even in your case it is good to use 64-bit if some of your apps fail due to lack of virtual address space (it is not a very common problem, but sometimes it happens).